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Simplifying x + 30x(x + 4) = 22 Reorder the terms: x + 30x(4 + x) = 22 x + (4 * 30x + x * 30x) = 22 x + (120x + 30x2) = 22 Combine like terms: x + 120x = 121x 121x + 30x2 = 22 Solving 121x + 30x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 121x + 30x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 121x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.7333333333 + 4.033333333x + x2 = 0 Move the constant term to the right: Add '0.7333333333' to each side of the equation. -0.7333333333 + 4.033333333x + 0.7333333333 + x2 = 0 + 0.7333333333 Reorder the terms: -0.7333333333 + 0.7333333333 + 4.033333333x + x2 = 0 + 0.7333333333 Combine like terms: -0.7333333333 + 0.7333333333 = 0.0000000000 0.0000000000 + 4.033333333x + x2 = 0 + 0.7333333333 4.033333333x + x2 = 0 + 0.7333333333 Combine like terms: 0 + 0.7333333333 = 0.7333333333 4.033333333x + x2 = 0.7333333333 The x term is 4.033333333x. Take half its coefficient (2.016666667). Square it (4.066944446) and add it to both sides. Add '4.066944446' to each side of the equation. 4.033333333x + 4.066944446 + x2 = 0.7333333333 + 4.066944446 Reorder the terms: 4.066944446 + 4.033333333x + x2 = 0.7333333333 + 4.066944446 Combine like terms: 0.7333333333 + 4.066944446 = 4.8002777793 4.066944446 + 4.033333333x + x2 = 4.8002777793 Factor a perfect square on the left side: (x + 2.016666667)(x + 2.016666667) = 4.8002777793 Calculate the square root of the right side: 2.190953623 Break this problem into two subproblems by setting (x + 2.016666667) equal to 2.190953623 and -2.190953623.Subproblem 1
x + 2.016666667 = 2.190953623 Simplifying x + 2.016666667 = 2.190953623 Reorder the terms: 2.016666667 + x = 2.190953623 Solving 2.016666667 + x = 2.190953623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.016666667' to each side of the equation. 2.016666667 + -2.016666667 + x = 2.190953623 + -2.016666667 Combine like terms: 2.016666667 + -2.016666667 = 0.000000000 0.000000000 + x = 2.190953623 + -2.016666667 x = 2.190953623 + -2.016666667 Combine like terms: 2.190953623 + -2.016666667 = 0.174286956 x = 0.174286956 Simplifying x = 0.174286956Subproblem 2
x + 2.016666667 = -2.190953623 Simplifying x + 2.016666667 = -2.190953623 Reorder the terms: 2.016666667 + x = -2.190953623 Solving 2.016666667 + x = -2.190953623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.016666667' to each side of the equation. 2.016666667 + -2.016666667 + x = -2.190953623 + -2.016666667 Combine like terms: 2.016666667 + -2.016666667 = 0.000000000 0.000000000 + x = -2.190953623 + -2.016666667 x = -2.190953623 + -2.016666667 Combine like terms: -2.190953623 + -2.016666667 = -4.20762029 x = -4.20762029 Simplifying x = -4.20762029Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.174286956, -4.20762029}
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